Beware striving for miniscule volume if weight also a factor.
I did much the same as you: riding to shipper's and packaging the bike into my pre-built crate on their site.
I took the obvious steps to reduce volume: remove front wheel, unbolt handlebars and rotate 90º, removed panniers - things you've already thought of.
My shipper's charges were based on volume and on weight, whichever was the greater.
When it came to calculating the shipping charge, it turned out that the weight-based charge was slightly greater than the volumetric-based charge, so I ultimately paid based on the actual weight of the bike and crate, not on its packaged volume.
So, for those of you using a shipper that uses a similar charging strategy, don't work yourself into a lather trying to squeeze your bike into the tiniest box imaginable; if actual weight enters the equation, then there will be a minimum volume, beyond which there's no gain in attempting to go.
Incidentally, I rested the front forks on the base of the crate, with a block of wood screwed to the base in front of the forks to prevent them sliding forward.
If thinking of using the front axle to take some of the weight, ensure that it's bearing the weight as close to the forks as possible (at positions similar to where the wheel bearings would contact the axle); don't place the support under the axle near the centre—this would be more likely to cause the axle to bend if the crate were dropped or handled roughly.
Best of luck,